12/18/2020

Batch Variables

## 
## SIEMENSPRISMAFIT   SIEMENSTIMTRIO     SIEMENSVERIO 
##               58             1185               36
## 
##  CHP  HSC  PNC 
##   36   58 1185

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##                   
##                     CHP  HSC  PNC
##   SIEMENSPRISMAFIT    0   58    0
##   SIEMENSTIMTRIO      0    0 1185
##   SIEMENSVERIO       36    0    0

Excluding HSC-SIEMENSTIMTRIO (n=7) for now.

## [1] "Batches:"
## [1] "CHP-SIEMENSVERIO"     "HSC-SIEMENSPRISMAFIT" "PNC-SIEMENSTIMTRIO"

Plot: Age

ANOVA: Age

## Analysis of Variance Table
## 
## Response: age
##             Df  Sum Sq Mean Sq F value    Pr(>F)    
## site         2  1012.5  506.27  34.606 2.313e-15 ***
## Residuals 1276 18667.2   14.63                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Age is confounded across sites.

Plot: Sex

Model: Sex

##      
##       FEMALE MALE
##   CHP     24   12
##   HSC     37   21
##   PNC    630  555
##      
##          FEMALE      MALE
##   CHP 0.6666667 0.3333333
##   HSC 0.6379310 0.3620690
##   PNC 0.5316456 0.4683544
## 
##  Pearson's Chi-squared test
## 
## data:  df$site and df$sex
## X-squared = 4.8976, df = 2, p-value = 0.0864

Layout

  1. Harmonization of intracraneal volume (ICV).

  2. Harmonization of 145 volumes

  3. ICV Normalization of 145 volumes

Harmonization method: ComBat (Johnson and Li (2007), Fortin et al. (2017), (2018)).

Layout: Options

  1. Harmonization of intracraneal volume (ICV).
    A. As single dataset.
    B. By Splitting data by Males and Females (M/F).

  2. Harmonization of 145 volumes
    A. As single dataset.
    B. By splitting data by Males and Females (M/F).
    C. By splitting data by tissues (Tissue).
    D. B + C.

  3. ICV Normalization of 145 volumes
    A. No adjustment.
    B. ICV Residualization: Splitting data by Males and Females (M/F).
    C. ICV Residualization: Joint (i.e. no M/F split).
    D. ICV as Covariate.

ICV (Raw)

ICV ~ Age [PNC]

Model: ICV ~ Age [PNC]

  ICV ICV [M] ICV [F]
Predictors Estimates Estimates Estimates
(Intercept) -0.50 *** -0.00 0.00
age 0.03 0.12 ** -0.05
sex [MALE] 1.08 ***
age2 -0.05 * -0.05 -0.07
Observations 1185 555 630
R2 / R2 adjusted 0.290 / 0.288 0.017 / 0.013 0.006 / 0.003
  • p<0.05   ** p<0.01   *** p<0.001

Model: ICV ~ Age [PNC, Males]

  ICV [M]
Predictors Estimates CI p
(Intercept) -0.00 -0.08 – 0.08 1.000
age 0.12 0.03 – 0.20 0.005
Observations 555
R2 / R2 adjusted 0.014 / 0.012
  ICV [F]
Predictors Estimates CI p
(Intercept) 0.00 -0.08 – 0.08 1.000
age -0.04 -0.12 – 0.04 0.348
Observations 630
R2 / R2 adjusted 0.001 / -0.000

Model: ICV ~ Age [PNC, Females]

  ICV
Predictors Estimates CI p
(Intercept) 0.00 -0.06 – 0.06 1.000
age -0.01 -0.07 – 0.04 0.635
Observations 1185
R2 / R2 adjusted 0.000 / -0.001

Batch contribution

## Analysis of Variance Table
## 
## Model 1: X702 ~ sex + age + age * sex
## Model 2: X702 ~ sex + age + age * sex + batch
##   Res.Df        RSS Df Sum of Sq      F  Pr(>F)   
## 1   1275 1.9996e+13                               
## 2   1273 1.9786e+13  2 2.099e+11 6.7524 0.00121 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Harmonized ICV

Harmonized ICV (adj. for sex)

Harmonized ICV (adj. for age)

Harmonized ICV (adj. for age, sex)

Batch contribution

## Analysis of Variance Table
## 
## Model 1: ICV ~ sex + age
## Model 2: ICV ~ sex + age + batch
##   Res.Df        RSS Df Sum of Sq      F Pr(>F)
## 1   1276 1.9760e+13                           
## 2   1274 1.9759e+13  2 753810856 0.0243  0.976

ICV Harmonization choice

Past this point, all reference to ICV refers to ICV harmonized by splitting data by sex (M/F; Option 1B).

WM total

WM total (adj. for age)

WM total (adj. for age + ICV)

M/F lines up residualized WM volumes best.

GM total

GM total (adj. for age)

GM total (adj for age + ICV)

M/F also performs the best on residualized GM volumes.

ROI Harmonization choice

Past this point, all reference to ROI refers refers to ROIs harmonized by splitting data by sex (M/F; Option 2B).

ANOVAs: M/F split harmonization

For each of the 145 ROI volumes, two models were used:
- Model 1: ROI ~ sex + age + agexsex (+ ICV)
- Model 2: ROI ~ sex + age + agexsex (+ ICV) + batch

Number of models for which batch variables contributes new information is shown below.

##              Raw    Raw (ICV adj)           Combat Combat (ICV adj) 
##               36               43                0                0

Correcting for ICV in volumes

ROIs are corrected for ICV with the formula
\[ROI_{adj} = ROI - \beta (ICV - \overline{ICV})\]
where \(\beta\) represents the ICV-ROI slope and \(\overline{ICV}\) is the average ICV of subjects in the cohort used for the correction (Nordenskjöld et al. 2015).

In this presentation, two cohorts (i.e. males and females) are corrected separately. Effects of using only one cohort are also shown.

PCA: Scree

(Covariance) PCA was performed with (M/F) ICV-corrected volumes. Then GM and WM totals were projected onto PCs 1 and 2.

PCA: Loadings

PCA: Contributions

Dimension 1

##       contr ROI_INDEX               ROI_NAME HEMISPHERE TISSUE_SEG
## 1 28.917845        81  frontal lobe WM right      Right         WM
## 2 28.259090        82   frontal lobe WM left       Left         WM
## 3  9.032425        87 temporal lobe WM right      Right         WM
## 4  8.372905        88  temporal lobe WM left       Left         WM
## 5  7.895716        86  parietal lobe WM left       Left         WM
## 6  7.033472        85 parietal lobe WM right      Right         WM

Dimension 2

##       contr ROI_INDEX                         ROI_NAME HEMISPHERE TISSUE_SEG
## 1 16.751181        38        Right Cerebellum Exterior      Right         GM
## 2 16.216717        39         Left Cerebellum Exterior       Left         GM
## 3  7.259439       142 Right MFG   middle frontal gyrus      Right         GM
## 4  6.548369       143  Left MFG   middle frontal gyrus       Left         GM
## 5  3.364917       169             Left PCu   precuneus       Left         GM
## 6  3.066817       168            Right PCu   precuneus      Right         GM

PCA: Circle of Correlations

Note: Blue lines denote supplementary projections.

PCA: Factor Scores

Sex differences are retained after ICV-residualizing by sex (M/F Residualization).

PCA: (Whole-Data ICV adj.)

Alternatively, GM loses contr. toward Dim 2 and sex differences are eliminated if ICV is residualized irrespective of sex (i.e. Joint Residualization).

Plot: WM (unadj.) ~ Age

Plot: WM (M/F Res.) ~ Age

Plot: WM (Joint Res.) ~ Age

Models: WM ~ Age

  WM WM (M/F Res.) WM (Joint Res.) WM
Predictors Estimates Estimates Estimates Estimates
(Intercept) -0.43 *** -0.66 *** 0.01 -8.54 ***
age 0.32 *** 0.55 *** 0.72 *** 0.36 ***
sex [MALE] 0.94 *** 1.43 *** -0.01 -0.02
age * sex [MALE] 0.14 ** 0.01 0.03 0.01
ICV 0.00 ***
Observations 1279 1279 1279 1279
R2 / R2 adjusted 0.335 / 0.333 0.737 / 0.736 0.542 / 0.541 0.889 / 0.889
  • p<0.05   ** p<0.01   *** p<0.001

In parentheses: ICV normalization method.

Model: WM ~ Age [Males]

  WM WM (M/F Res.) WM (Joint Res.) WM
Predictors Estimates Estimates Estimates Estimates
(Intercept) 0.47 *** 0.72 *** -0.08 ** -8.57 ***
age 0.46 *** 0.55 *** 0.74 *** 0.36 ***
age2 -0.07 -0.02 -0.04 -0.02
ICV[M_filter] 0.00 ***
Observations 588 588 588 588
R2 / R2 adjusted 0.229 / 0.226 0.515 / 0.513 0.528 / 0.526 0.872 / 0.871
  • p<0.05   ** p<0.01   *** p<0.001

Model: WM ~ Age [Females]

  WM WM (M/F Res.) WM (Joint Res.) WM
Predictors Estimates Estimates Estimates Estimates
(Intercept) -0.40 *** -0.61 *** 0.07 ** -8.49 ***
age 0.33 *** 0.55 *** 0.73 *** 0.36 ***
age2 -0.10 ** -0.06 *** -0.08 *** -0.04 **
ICV[F_filter] 0.00 ***
Observations 691 691 691 691
R2 / R2 adjusted 0.157 / 0.154 0.557 / 0.555 0.557 / 0.556 0.859 / 0.859
  • p<0.05   ** p<0.01   *** p<0.001

Plot: GM (unadj.) ~ Age

Plot: GM (M/F Res.) ~ Age

Plot: GM (Joint Res.) ~ Age

Model: GM ~ Age

  GM GM (M/F Res.) GM (Joint Res.) GM (Joint Cov.)
Predictors Estimates Estimates Estimates Estimates
(Intercept) -0.47 *** -0.68 *** -0.07 * -8.34 ***
age -0.34 *** -0.45 *** -0.70 *** -0.31 ***
sex [MALE] 1.04 *** 1.48 *** 0.15 *** 0.10 ***
age * sex [MALE] 0.12 ** -0.00 -0.02 -0.00
ICV 0.00 ***
Observations 1279 1279 1279 1279
R2 / R2 adjusted 0.384 / 0.383 0.806 / 0.806 0.518 / 0.517 0.906 / 0.906
  • p<0.05   ** p<0.01   *** p<0.001

Model: GM ~ Age [Males]

  GM GM (M/F Res.) GM (Joint Res.) GM (Joint Cov.)
Predictors Estimates Estimates Estimates Estimates
(Intercept) 0.59 *** 0.84 *** 0.15 *** -8.42 ***
age -0.22 *** -0.44 *** -0.71 *** -0.31 ***
age2 -0.03 0.03 0.06 0.02
ICV[M_filter] 0.00 ***
Observations 588 588 588 588
R2 / R2 adjusted 0.068 / 0.064 0.489 / 0.487 0.502 / 0.500 0.866 / 0.865
  • p<0.05   ** p<0.01   *** p<0.001

Model: GM ~ Age [Females]

  GM GM (M/F Res.) GM (Joint Res.) GM (Joint Cov.)
Predictors Estimates Estimates Estimates Estimates
(Intercept) -0.50 *** -0.72 *** -0.13 *** -8.24 ***
age -0.35 *** -0.45 *** -0.71 *** -0.32 ***
age2 -0.02 0.06 *** 0.10 *** 0.04 ***
ICV[F_filter] 0.00 ***
Observations 691 691 691 691
R2 / R2 adjusted 0.177 / 0.175 0.532 / 0.530 0.526 / 0.524 0.871 / 0.870
  • p<0.05   ** p<0.01   *** p<0.001

References

<Insert references for Combat and ICV-normalization.>

Fortin, Jean Philippe, Nicholas Cullen, Yvette I. Sheline, Warren D. Taylor, Irem Aselcioglu, Philip A. Cook, Phil Adams, et al. 2018. “Harmonization of cortical thickness measurements across scanners and sites.” NeuroImage 167 (November 2017). Elsevier Ltd: 104–20. https://doi.org/10.1016/j.neuroimage.2017.11.024.

Fortin, Jean Philippe, Drew Parker, Birkan Tunç, Takanori Watanabe, Mark A. Elliott, Kosha Ruparel, David R. Roalf, et al. 2017. “Harmonization of multi-site diffusion tensor imaging data.” NeuroImage 161 (March). Elsevier Ltd: 149–70. https://doi.org/10.1016/j.neuroimage.2017.08.047.

Johnson, W Evan, and Cheng Li. 2007. “Adjusting batch effects in microarray expression data using empirical Bayes methods,” 118–27. https://doi.org/10.1093/biostatistics/kxj037.

Nordenskjöld, Richard, Filip Malmberg, Elna Marie Larsson, Andrew Simmons, Håkan Ahlström, Lars Johansson, and Joel Kullberg. 2015. “Intracranial volume normalization methods: Considerations when investigating gender differences in regional brain volume.” Psychiatry Research - Neuroimaging 231 (3). Elsevier: 227–35. https://doi.org/10.1016/j.pscychresns.2014.11.011.